# Delay Differential Equations: With Applications in Population Dynamics

@inproceedings{Kuang2012DelayDE, title={Delay Differential Equations: With Applications in Population Dynamics}, author={Y. Kuang}, year={2012} }

Delay Differential Equations: Introduction. Basic Theory of Delay Differential Equations. Characteristic Equations. Applications in Population Dynamics: Global Stability for Single Species Models. Periodic Solutions, Chaos, Stage Structures, And State Dependent Delays in Single Species Models. Global Stability for Multi-Species Models. Periodic Solutions in Multi-Species Models. Permanence. Neutral Delay Models. References. Appendix. Index.

#### 2,087 Citations

Stability conditions for a class of delay differential equations in single species population dynamics

- Mathematics
- 2012

We consider a class of nonlinear delay differential equations,which describes single species population growth with stage structure. By constructing appropriate Lyapunov functionals, the global… Expand

Global stability and Hopf bifurcation of a plankton model with time delay

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- 2010

Abstract A differential delay equation model with a discrete time delay and a distributed time delay is introduced to simulate zooplankton–nutrient interaction. The differential inequalities’ methods… Expand

ASYMPTOTIC STABILITY OF DELAY DIFFERENTIAL EQUATIONS VIA FIXED POINT THEORY AND APPLICATIONS

Nonlinear delay differential equations have been widely used to study the dynamics in biology, but the stability of such equations are challenging. In this paper, new criteria are established for the… Expand

DELAYS INDUCED IN POPULATION DYNAMICS

This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to… Expand

Periodic solution of a neutral delay model of single-species population growth on time scales⋆

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- 2010

By using a fixed point theorem of strict-set-contraction, we present some sufficient conditions for the existence of at least one positive ω-periodic solution to a neutral delay model of… Expand

Stability and Bifurcation in a Diffusive Logistic Population Model with Multiple Delays

- Computer Science, Mathematics
- Int. J. Bifurc. Chaos
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A diffusive logistic population model with multiple delays and Dirichlet boundary condition and the stability/instability of the positive equilibrium and delay induced Hopf bifurcation are investigated. Expand

Stability criteria for the system of delay differential equations and its applications

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- 2019

In this paper, we consider the asymptotic stability for the system of linear delay differential equations. Because of the complicated interactions induced by the delay effects of the system, there… Expand

Multiple Periodic Solutions of Nonlinear Functional Differential Equations

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The existence of two positive periodic solutions of first order functional differential equations with nondecreasing nonlinear terms is proved. The results are applied to the logistic equation of… Expand

Chaos in delay differential equations with applications in population dynamics

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We develop a geometrical method to detect the presence of chaotic
dynamics in delay differential equations. An application to the
classical Lotka-Volterra model with delay is given.

Positive Periodic Solutions in a Discrete Time Three Species Competition System

- Mathematics, Computer Science
- J. Appl. Math.
- 2013

Using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive periodic solutions of the model are obtained. Expand